I made some chain-mail using knots instead of rings for links. One sample uses carrick mats, which have four loops on the outside and so attach to four others, but the other uses simple overhand "trefoil" knots which only link to three others, causing it to form a really cool-looking hexagonal sort of pattern, when stretched out. Check 'em out!

Can you use a physics engine to collapse them down to compress the space they take up during building, so they come out the printer as a big lump and then they fluff up when you pull them out?

That would be great, and help achieve high density, which I know is a Good Thing in terms of pricing. It surely should be possible... if I knew my way around the physics engine of Blender better than I do (which is not at all).

The trefoil mail compresses nicely (hard to get it to lie flat, in fact, but the carrick mail has a tendency to form "kinks" when bent that have to be coaxed back to flat again. Not everywhere, not every time, and it isn't hard to shake them back, but it doesn't compress down well.